The unconstrained binary quadratic programming problem: a survey

In recent years the unconstrained binary quadratic program (UBQP) has grown in importance in the field of combinatorial optimization due to its application potential and its computational challenge. Research on UBQP has generated a wide range of solution techniques for this basic model that encompasses a rich collection of problem types. In this paper we survey the literature on this important model, providing an overview of the applications and solution methods.     

Population growth and the birth squeeze

Birth squeezes result from an imbalance in the number of males and females in the childbearing ages, and can have a significant impact on the level and distribution of births. To measure the effects of a birth squeeze, the observed male and female age-specific birth rates were distinguished from the underlying fertility magnitudes, which reflect the mutual propensity of males and females of specified ages to have a child. The fertility magnitudes, readily expressible in terms of the birth rates, are nonetheless independent of the age-sex composition of the population, while the birth rates are affected by compositional changes. The two-sex Total Fertility Rate, TFR2, the average of the male and female TFRs, is advanced as a summary measure of fertility independent of the birth squeeze, and a simple index, U, is defined to measure the severity of the squeeze. Analyses involving stable population models, alternative population projections, and the birth squeezes found in contemporary populations documented the importance of the birth squeeze for studies of fertility. In particular, the size of the distortions introduced by the birth squeeze was seen as related to the level of fertility itself. In high-fertility populations, the birth squeeze depresses observed female age-specific birth rates, and thus conventional measures can significantly underestimate the fertility reduction needed to end population growth.     

Mindfulness‐Based Relationship Education for Couples Expecting their First Child—Part 2: Phenomenological Findings

This phenomenological study is the second phase of a larger mixed methods study of a relationship‐enhancement program for couples expecting their first child (see Gambrel & Piercy, this issue). The 4‐week Mindful Transition to Parenthood Program uses mindfulness practices and interpersonal activities to develop skills of internal and interpersonal attunement. Based on semi‐structured interviews with thirteen couples, four overarching themes emerged: (a) positive changes for self, (b) improvements in couple relationship, (c) more prepared for baby, and (d) male involvement. Participants stated that the program increased their acceptance and awareness, deepened connections with their partners, and led them to be more confident about becoming parents. Male participants felt they became more identified as fathers. The authors discuss the clinical implications of these findings. Video Abstract     

A MODEL FOR THE PREDICTION OF JUROR DECISIONS*

A logit model approach designed to assign a probability whether prospective jurors will favor the defendant or plaintiff in a case, as a function of perceived individual juror characteristics, is described in the context of a case situation. The model, which has been programmed on a hand-held computer, is designed for implementation in courtroom settings to help defense attorneys evaluate and select jurors in order to minimize the likelihood of large jury awards. Empirical tests of the model are also described.     

Confirmatory Factor Analysis of Ordinal Data Using Full‐Information Adaptive Quadrature

We conducted confirmatory factor analysis (CFA) of responses (N=803) to a self‐reported measure of optimism, using full‐information estimation via adaptive quadrature (AQ), an alternative estimation method for ordinal data. We evaluated AQ results in terms of the number of iterations required to achieve convergence, model fit, parameter estimates, standard errors (SE), and statistical significance, across four link‐functions (logit, probit, log‐log, complimentary log‐log) using 3–10 and 20 quadrature points. We compared AQ results with those obtained using maximum likelihood, robust maximum likelihood, and robust diagonally weighted least‐squares estimation. Compared to the other two link‐functions, logit and probit not only produced fit statistics, parameters estimates, SEs, and levels of significance that varied less across numbers of quadrature points, but also fitted the data better and provided larger completely standardised loadings than did maximum likelihood and diagonally weighted least‐squares. Our findings demonstrate the viability of using full‐information AQ to estimate CFA models with real‐world ordinal data.     

A test for multivariate structure

We present a test for detecting 'multivariate structure' in data sets. This procedure consists of transforming the data to remove the correlations, then discretizing the data and, finally, studying the cell counts in the resulting contingency table. A formal test can be performed using the usual chi-squared test statistic. We give the limiting distribution of the chi-squared statistic and also present simulation results to examine the accuracy of this limiting distribution in finite samples. Several examples show that our procedure can detect a variety of different types of structure. Our examples include data with clustering, digitized speech data, and residuals from a fitted time series model. The chi-squared statistic can also be used as a test for multivariate normality.     

Optimizing Service Attributes: The Seller's Utility Problem*

Service designers predict market share and sales for their new designs by estimating consumer utilities. The service's technical features (for example, overnight parcel delivery), its price, and the nature of consumer interactions with the service delivery system influence those utilities. Price and the service's technical features are usually quite objective and readily ascertained by the consumer. However, consumer perceptions about their interactions with the service delivery system are usually far more subjective. Furthermore, service designers can only hope to influence those perceptions indirectly through their decisions about nonlinear processes such as employee recruiting, training, and scheduling policies. Like the service's technical features, these process choices affect quality perceptions, market share, revenues, costs, and profits. We propose a heuristic for the NP‐hard service design problem that integrates realistic service delivery cost models with conjoint analysis. The resulting seller's utility function links expected profits to the intensity of a service's influential attributes and also reveals an ideal setting or level for each service attribute. In tests with simulated service design problems, our proposed configurations compare quite favorably with the designs suggested by other normative service design heuristics.     

Analyzing and Modeling the Maximum Diversity Problem by Zero-One Programming*

The problem of maximizing diversity deals with selecting a set of elements from some larger collection such that the selected elements exhibit the greatest variety of characteristics. A new model is proposed in which the concept of diversity is quantifiable and measurable. A quadratic zero-one model is formulated for diversity maximization. Based upon the formulation, it is shown that the maximum diversity problem is NP-hard. Two equivalent linear integer programs are then presented that offer progressively greater computational efficiency. Another formulation is also introduced which involves a different diversity objective. An example is given to illustrate how additional considerations can be incorporated into the maximum diversity model.